A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants

Short-term scheduling of multipurpose batch plants is a challenging problem for which several formulations exist in the literature. In this paper, we present a new, simpler, more efficient, and potentially tighter, mixed integer linear programming (MILP) formulation using a continuous-time representation with synchronous slots and a novel idea of several balances (time, mass, resource, etc.). The model uses no big-M constraints, and is equally effective for both maximizing profit and minimizing makespan. Using extensive, rigorous numerical evaluations on a variety of test problems, we show that in contrast to the best model in the literature, our model does not decouple tasks and units, but still has fewer binary variables, constraints, and nonzeros, and is faster.